A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence

• Published in: International journal for numerical methods in engineering Vol. 122; no. 24; pp. 7409 - 7430
• Main Authors: Jelich, Christopher, Koji Baydoun, Suhaib, Voigt, Matthias, Marburg, Steffen
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.12.2021; Wiley Subscription Services, Inc
• Subjects: Acoustics; Algorithms; Boundary element method; Domains; Elastodynamics; Finite element method; greedy algorithm; Greedy algorithms; implicit parameter dependence; Parameters; reduced basis; Sound pressure; Spherical shells; structural acoustic interaction
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6835

In this article, a greedy reduced basis algorithm is proposed for the solution of structural acoustic systems with parameter and implicit frequency dependence. The underlying equations of linear time‐harmonic elastodynamics and acoustics are discretized using the finite element and boundary element method, respectively. The solution within the parameter domain is determined by a linear combination of reduced basis vectors. This basis is generated iteratively and given by the responses of the structural acoustic system at certain parameter samples. A greedy approach is followed by evaluating the next basis vector at the parameter sample which is currently approximated worst. The algorithm runs on a small training set which bounds the memory requirements and allows applications to large‐scale problems with high‐dimensional parameter domains. The computational efficiency of the proposed scheme is illustrated based on two numerical examples: a point‐excited spherical shell submerged in water and a satellite structure subject to a diffuse sound pressure field excitation.